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Solving Equations – Do/Undo Method
Ex. 1)
2x – 3 = -7
Do
Undo
∙2
÷2
–3
+3
The variable “x” is first being multiplied by 2
and then that product is being subtracted
by 3. To solve this equation, we must not
only reverse operations used to create the
equation, but also the order of these
operations. Since subtracting 3 was the last
step in creating the equation, the first step
in solving would be to add 3. Then we
would undo the multiplying by 2 by dividing
by 2. Following the arrows will help
students solve the equation.
2x – 3 = -7
+ 3 +3
First step, add 3 to both sides.
2x – 3 = -7
+ 3
+3
Minus three plus three combine to give zero.
Shannon Richards
2x
= -4
2x
2
= -4
2
Second step, divide both sides by 2,
2x
2
= -4
2
Any number divided by itself equals one.
x
= -2
Solution
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Solving Equations – Do/Undo Method
Ex. 2)
x+5=6
4
Do
Undo
÷4
∙4
+5
-5
x
4
+ 5 =
6
First step, subtract 5 from both sides.
– 5
x
4
The variable “x” is first being divided by 4
and then that quotient is being added to 5.
Since adding 5 was the last step in creating
the equation, the first step in solving would
be to subtract 5. Then we would undo the
dividing by 4 by multiplying by 4.
– 5
+ 5 =
– 5
6
– 5
x
4
=
1
4 ∙ x
4
=
1 ∙ 4
Add five subtract five combine to give zero.
1
1
x
Shannon Richards
= 4
The 4’s simplify to 1 on the diagonal. Even if
4x is divided by 4, 1x will result on the left of
the equals sign.
Solution
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Solving Equations – Do/Undo Method
Ex. 3.A)
3 x – 2 = -8
5
Do
Undo
∙3
÷5
–2
÷3
∙5
+2
3 x – 2 = -8
5
+ 2 + 2
3 x – 2 = -8
5
+ 2 + 2
3x
5
=
-6
5 ∙ 3x
5
=
-6 ∙ 5
1
Shannon Richards
1
The variable “x” is first being multiplied by
3, and then the product is being divided by
5. Finally, the quotient is being subtracted
by 2. Since subtracting 2 was the last step in
creating the equation, the first step in
solving would be to add 2. Then we would
undo the dividing by 5 by multiplying by 5.
Finally, to undo the multiplication by 3, we
would divide by 3.
Add 2 to both sides of the equation.
Subtract two add two combine to give zero.
The 5’s simplify to 1 on the diagonal. Even if
15x is divided by 5, 3x will result on the left
of the equals sign.
3x
= -30
3x
3
= -30
3
Divide by 3 on both sides.
x
= -10
Solution
Page 3
Solving Equations – Do/Undo Method
The last example could be illustrated using only two operations instead of three. This would be
essential to show students in order to emphasize the flexibility in solving. Here is the last
example worked with a fractional coefficient to the variable.
Ex. 3.B)
The variable “x” is first being multiplied by
x – 2 = -8
, and then product is being subtracted by
Do
2. Since subtracting 2 was the last step in
creating the equation, the first step in
solving would be to add 2. Then we would
Undo
∙
÷
undo the multiplication by
or ∙
by dividing by
, or rather multiplying by its reciprocal.
–2
+2
x – 2 = -8
+ 2
Add 2 to both sides of the equation.
+ 2
x – 2 = -8
+ 2
x
Subtract two add two combine to give zero.
+ 2
=
-6
-2
∙
x
=
Multiply both sides by the reciprocal and
simplify.
∙
1
1
x
Shannon Richards
= -10
Solution
Page 4